Method and apparatus for obtaining high-resolution x-ray interference patterns

ABSTRACT

A high-resolution X-ray interferometer. The invention utilizes nonlocalized conical interference fringes which are formed when X-rays from a point source fall on a three-dimensional, planar crystalline array. Each atom within the crystal scatters radiation which then appears to originate from a set of virtual sources S1, S2, S3, ..., Sn located on a line perpendicular to the scattering planes of the crystal. At any point P&#39;&#39; behind the point source (for a reflection arrangement) X-rays are received from S1, S2, S3, ..., Sn and interfere to form fringes, analogous to the familiar conical fringes in optics. If and only if the crystal or film of crystallites is thin and less than a certain thickness will interference fringes be formed at P&#39;&#39;. Since the fringes are nonlocalized, no optics are required to produce any focusing. The structure of the fringes reveals the structure, not of the crystal, but of the X-ray spectra. By having large crystal-to-detector distances extremely large dispersions can be realized.

United States Patent Colin S. Willett Washington, D.C.

[21} Appl. No. 54,272

[22] Filed July 13, 1970 [45] Patented Dec. 21,1971

[73] Assignee The United States of America as represented by theSecretary of the Army [72] Inventor [54] METHOD AND APPARATUS FOROBTAINING HIGH-RESOLUTION X-RAY INTERFERENCE Primary Examiner-Anthony L.Birch AttorneysI-Iarry M. Saragovitz, Edward J. Kelly, Herbert Berl andJ. D. Edgerton ABSTRACT: A high-resolution X-ray interferometer. Theinvention utilizes nonlocalized conical interference fringes which areformed when X-rays from a point source fall on a three-dimensional,planar crystalline array. Each atom within the crystal scattersradiation which then appears to originate from a set of virtual sources8,, S S S, located on a line perpendicular to the scattering planes ofthe crystal. At any point P behind the point source (for a reflectionarrangement) X-rays are received from S S S S, and interfere to formfringes, analogous to the familiar conical fringes in optics. If andonly if the crystal or film of crystallites is thin and less than acertain thickness will interference fringes be formed at P. Since thefringes are nonlocalized, no optics are required to produce anyfocusing. The structure of the fringes reveals the structure, not of thecrystal, but of the X-ray spectra. By having large crystal-to-detectordistances extremely large dispersions can be realized.

PATENTEUBEBZI am 3529.580

SHEET 2 OF 2 flTTOFA/EYS METHOD AND APPARATUS FOR OBTAINING HIGH-RESOLUTION X-RAY INTERFERENCE PATTERNS RIGHTS OF GOVERNMENT Theinvention described herein may be manufactured, used, and licensed by orfor the United States Government for governmental purposes without thepayment to me of any royalty thereon.

BACKGROUND OF THE INVENTION 1. Field of the Invention This inventionrelates to X-ray interferometers and more particularly to a device andmethod for the precision measurement of X-ray absorption edges andemission lines in the X- ray spectral region.

2. Description of the Prior Art Analysis of low energy X-ray spectra ispresently achieved by using single or double crystal spectrometers inwhich Bragg diffraction determines whether or not X-rays scattered fromthe analyzing crystal of the spectrometer emerge as beams from thecrystal. Due to the interference between the scattered radiation fromthe multitude of scattering atoms, scattered radiation emerges from acrystal as a beam only when the Bragg law n).=2d sin is satisfied andwhen the incident X- ray beam is nondivergent. Following X-rayconvention, 0 is the angle between the incident X-ray beam and thelattice planes of the crystal, n is the order of reflection, A is thewavelength, and d is the known distance between the parallel planes inthe crystal. The angle 0 is then the complement of the incident angleconventionally used in optics. Since the incident X-ray beam isparallel, the width of a spectral line is determined by the size of thecollimating pinhole or slit. In optical spectrometers the resolution isalso determined to a large extent by the diffraction limitation set bythe slit. No such dependence applies when interferometric techniques areused. The best available low energy X-ray spectrometers have notachieved resolutions greater than 4.5X. Because the refractive index ofmaterials in the X-ray region is very closely unity, X-rays cannot befocused like visible radiation. Therefore, a simple system that wouldprovide nonlocalized large dispersion, high-resolution X-ray spectrawould be highly desirable.

Accordingly, the primary object of the present invention is to providean X-ray interferometer in which extremely large dispersions and highresolutions can be realized.

Another object of the present invention is to provide a method forobtaining X-ray interference patterns which does not rely onbeamsplitting or crystal difiraction techniques normally used for X-rayinvestigation.

A further object of the present invention is to provide an X- rayinterferometer that utilizes nonlocalized conical fringes to analyze thestructure of the X-ray spectra.

SUMMARY OF THE INVENTION Briefly, in accordance with the invention, amethod and apparatus for obtaining high-resolution X-ray interferencepatterns is provided. The apparatus comprises a point source of X-rays,a planar crystal or a membrane coated with fine crystallites which havea suitable crystalline lattice spacing, and a detector which can be anarray of detectors, a single detector or a photographic plate. Dependingon the crystalline spacing of the crystal or crystallites the thicknessof the crystal must not exceed a certain length, referred to herein asthe coherence length. The X-rays from the point source are directed ontothe crystal whose atoms scatter the radiation, thereby creating a set ofvirtual sources. X-rays received from the virtual sources interferenceto produce fringes on the detector that are closely similar to theFabry-Perot fringes produced in optics. The nonlocalized character ofthe fringes produced thereby obviate the need for optical focusingapparatus. In this invention the many scattering centers of the atomsreplace the multiple reflections between two mirror surfaces used inFabry-Perot etalons. By utilizing the method and apparatus presentedherein, resolutions of greater than [0* are realizable along withextremely large dispersions.

BRIEF DESCRIPTION OF THE DRAWINGS The specific nature of the inventionas well as other aspects, uses, and advantages thereof will clearlyappear from the following description and from the accompanyingdrawings, in which:

FIG. 1 illustrates the basic arrangement of the X-ray interferometer ofthe present invention; and

FIG. 2 shows an expanded and simplified view of FIG. 1 illustrating theformation of the nonlocalized conical fringes according to the presentinvention.

DESCRIPTION OF THE PREFERRED EMBODIMENT There exists in optics a deviceknown as a Fabry-Perot etalon which is a multiple reflectioninterferometer of very high resolving power that is utilized to producebright interference fringes for the detailed study of the hyperfinestructure of visible spectrum lines. In the Fabry-Perot etalon, anextended source is commonly used which requires a collecting element,i.e., a lens, to bring the emergent parallel beams to a focus to formthe interference fringes. A practical collecting element for X-rays doesnot exist so that one cannot use the Fabry-Perot etalon arrangement withan extended source for the analysis of X-ray spectra.

There is, however, in optics a type of interference fringe calledconical fringes which are practically identical to Fabry- Perot fringesyet which do not require collecting elements to form them. See, forexample, Multiple Beam Interferometry, S. Tolansky, Clarendon Press,Oxford, 1949, 2nd edition, pp. 8-l 3. These multiple beam nonlocalizedfringes are formed by light from a point source making multiplereflections at an airdielectric boundary and have been used extensivelyby Tolansky in studies of cleavage steps on samples of mica. The fringeshave the property of enormous dispersion combined with the highresolution of Fabry-Perot fringes. l have discovered that nonlocalizedX-ray fringes in reflection, directly analogous to the nonlocalizedfringes used by Tolansky, can be observed with X-rays.

Referring now to FIG. 1, the basic apparatus of the X-ray interferometeris seen to consist of a point source of X-rays 10, a suitable crystal12, and a plane of detectors or a photographic plate 14. Point source 10directs a spherical wave front of radiation as represented by rays 20directly onto crystal 12. In this arrangement, a shield 16 is needed toprevent the radiation from source 10 from impinging directly upondetector 14. A suitable filter 18 may be placed in the path of theX-rays emanating from source 10 to isolate single spectrum lines forobservation on plate 14. Alternatively, a coherent monochromatic beammay be utilized as source 10 to obviate the need for filter 18 when itis desired to study the hyperfine structure of single spectrum lines.Crystal 12 is a good quality laminar type crystal such as mica, or canbe a membrane coated with a thin layer of crystallites, whose thicknessmust not be more than a predefined amount, referred to hereinafter asthe coherence length. The conical fringes are formed on detector 14 and22, 24 and 26 as a result of the multiple scattering of the X-rays bythe atoms in crystal l2, explained more fully hereinafter.

FIG. 2 shows an exaggerated view of the apparatus of FIG. 1 in which theeffects of the multiple scattering of the X-rays from point source 10are apparent. Crystal I2, shown greatly enlarged, has a series of nvertical scattering planes numbered 1, 2, 3, n. These scattering planesare shown to be perpendicular to the center ray 30 of the X-rayradiation emanating from point source 10, but it is understood thatthese planes may be oriented in any suitable manner with similarresults. The thickness of crystal 12 is indicated in FIG. 2 by d, andthe distance between successive scattering planes within crystal I2 isindicated by z.

The multiple scattering of the X-rays from point source 10 that occursat each atom, considered to be located at lattice points, produces ineffect a series of virtual sources 8,, S S S, at separations equal to2!, i.e., twice the spacing between the scattering planes in thecrystal. This means that any point P on detector 14 can be reached fromany of the virtual sources 8,, 8,, 8,, S, so that a nonlocalizedinterference fringe pattern will be formed in front of the crystal. Eachvertical scattering plane in crystal 12 in effect creates its ownvirtual source located on a line perpendicular to the scattering planes.For example, if we consider X-ray 22 from point source 10 to impingeupon atom 40 and X-ray 24 from source 10 to impinge upon atom 42, theeffect of the path differences in the scattered radiation from atoms 40and 42 at point P on detector 14 is the same as the interference whichwould be created by radiation emanating from virtual source 8,. This istrue due to the fact that the path distance from source 10 to atoms 40and 42, both located in plane 3 of crystal 12, is the same as the pathdistance from atoms 40 and 42 to virtual source 8,. In this way, it isseen that for each scattering plane in crystal 12, there will exist avirtual source located on the line perpendicular to the scatteringplanes. The resultant interference fringe located at any point P ondetector 14 is a result of the path differences in the scatteredradiation from the different scattering planes within crystal 12 or,alternatively, a result of the path differences in the radiationemanating from virtual sources 8,, 8,, S S,,.

Paralleling the development given by Tolansky, ibid., chapter 15, pp.171-177, the path difference D, between point P and the virtual sourcesS and S,, is given by D,,=2nrcos0+2n(t/L)sinlicost) 1 The refractiveindex of crystal [2 is taken to be unity, n is the number of the virtualsource, 2 is the scattering plane spacing and L is the distance betweenvirtual source S, and detector 14. if 1), equals nlt, where n is aninteger, constructive interference occurs and a bright fringe will beformed at point P. The first term in the above equation is thedifference in optical paths between two emerging parallel beams from twosources, corresponding to that applying in a Fabry-Perot etalon where toform a localized interference fringe pattern a lens must be used tobring emergent coherent parallel beams to a focus. The second term inthe above equation is the optical path difference between S P and S P,since the nonlocalized fringe pattern is produced by nonparallel beams"which do not need to be collected to form interference fringes.

Since the rays emanating from the virtual sources S S S S,,, are notparallel, there will be a phase difference by which the nth ray lagsbehind the first ray over that of the first term in equation l The lag Ais given by A=2(n -l )(F/L) sinOcosO (2) As long as A is less than M2,nondestructive interference will occur at P' at values of 9 given by theBragg Law (and the Fabry-Perot condition) to give a nonlocalizedcircular interference fringe pattern concentric with the normal betweenpoint source 10 and the crystal scattering planes. If we take as anexample the detector 14 being located such that is approximately equalor less than 35, the requirement for fringe formation is that A=(n--l)(t/2L)(lt/2). Taking a practical case of )t==lA., a scattering planespacing t of mica of 20A. and a source-to-detector distance L of 10 cm.,A is less than A/2 for n s(LA/f or nsljxlfl The thickness of d of micarequired to give this number of scattering planes, that is the number ofvirtual sources 8,, S S S,,, is approximately 3.0Xl0 cm. This is apractical crystal thickness. To reiterate, the path difference A betweenP'S and PS, must not approach A/Z for the fringes to form, i.e., as thepaths between P'S PS PS etc., are not quite equal increments, a certaincoherence length given by d= must not be exceeded.

For the above example, the angular separation of the fringes that areformed will be approximately 12. Since the number of virtual sourceswhich contribute to the intensity of a fringe at point P is on the orderof 1.5X", the finesse F of the interferometer, where F is effectivelythe number of interfering beams, will also be on the order of 10 1 hiswill result in a resolution close to 10. Since L can be made much largerthan that of 10 cm. chosen above for illustration. this figure for theresolution can be improved considerably. The resolution achievable usingthis method is better than that currently obtained with two crystalspectrometer techniques. Additionally, the technique will lend itself toutilization in space-science applications where simplicity, smallnessand ruggedness combined with high resolution are a considerableadvantage. Because the fringes are nonlocalized, no optics are requiredto produce any focusing. The structure of the fringes reveals thestructure, not of the crystal, but of the X-ray spectra. In thisinvention, the many scattering centers of the atoms in the crystalreplace the multiple reflections between two mirror surfaces used inFabry-Perot etalons. Such fringes formed by the interferometer of thepresent invention have only been used heretofore in optics, and Ibelieve that heretofore they have not been observed with radiation otherthan light.

[wish it to be understood that I do not desire to be limited to theexact details of construction shown and described, for obviousmodifications will occur to a person skilled in the art.

I claim as my invention:

1. An X-ray interferometer, comprising:

a. a point source of X-ray radiation;

b. means for forming nonlocalized conical interference fringes for theanalysis of said X-ray radiation comprising a laminar crystal notexceeding a prespecified thickness and having a plurality of parallelscattering planes onto which said X-ray radiation is directed and withinwhich each atom scatters said X-ray radiation; and

c. detection means noncoplanar with said point source for receiving anddetecting said nonlocalized conical inter ference fringes formed due tothe path differences of said scattered radiation from each of saidscattering planes to said detection means.

2. The invention according to claim 1 wherein said interference fringesreceived by said detection means appear to originate from a plurality ofvirtual sources located on a line perpendicular to said scatteringplanes, the number of said virtual sources being equal to the number ofscattering planes within said laminar crystal.

3. The invention according to claim 2 wherein said prespecifiedthickness is defined by one-half of the square root of the product ofthe detector-to-crystal distance and the scattering plane separation.

4. The invention according to claim 3 wherein the distance betweensuccessive virtual sources is equal to twice the distance betweensuccessive scattering planes.

5. The invention according to claim 4 wherein said detection means islocated behind said point source of X-ray radiation and parallel to saidscattering planes, said radiation from said point source being shieldedfrom impinging directly upon said detection means.

6. The invention according to claim 4 further comprising an X-ray filterpositioned between said point source and said laminar crystal forisolating desired spectrum lines of said X- ray radiation forobservation upon said detection means.

7. The invention according to claim '4 wherein said detection meanscomprises a photographic plate.

8. The invention according to claim 4 wherein said detection meanscomprises an array of X-ray detectors.

9. A method of obtaining X-ray interference patterns, comprising thesteps of:

a. directing a coherent monochromatic beam of X-rays from a point sourceonto a highly perfect laminar crystal not exceeding a prespecifiedthickness and having a plurality of parallel scattering planes therein;

b. scattering said X-rays in all directions by the atoms within saidscattering planes; and

c. positioning a detector parallel to said scattering planes of saidcrystal so as to receive the scattered radiation therefrom and whereonnonlocalized conical interference fringes are detected by virtue of thepath differences of the scattered radiation between the detector andeach of said scattering planes.

10. The invention according to claim 9 wherein said prespecifiedthickness is defined by one-half of the square root of the product ofthe detector-to-crystal distance and the scatter plane separation.

1. An X-ray interferometer, comprising: a. a point source of X-rayradiation; b. means for forming nonlocalized conical interferencefringes for the analysis of said X-ray radiation comprising a laminarcrystal not exceeding a prespecified thickness and having a plurality ofparallel scattering planes onto which said X-ray radiation is directedand within which each atom scatters said X-ray radiation; and c.detection means noncoplanar with said point source for receiving anddetecting said nonlocalized conical interference fringes formed due tothe path differences of said scattered radiation from each of saidscattering planes to said detection means.
 2. The invention according toclaim 1 wherein said interference fringes received by said detectionmeans appear to originate from a plurality of virtual sources located ona line perpendicular to said scattering planes, the number of saidvirtual sources being equal to the number of scattering planes withinsaid laminar crystal.
 3. The invention according to claim 2 wherein saidprespecified thickness is defined by one-half of the square root of theproduct of the detector-to-crystal distance and the scattering planeseparation.
 4. The invention according to claim 3 wherein the distancebetween successive virtual sources is equal to twice the distancebetween successive scattering planes.
 5. The invention according toclaim 4 wherein said detection means is located behind said point sourceof X-ray radiation and parallel to said scattering planes, saidradiation from said point source being shielded from impinging directlyupon said detection means.
 6. The invention according to claim 4 furthercomprising an X-ray filter positioned between said point source and saidlaminar crystal for isolating desired spectrum lines of said X-rayradiation for observation upon said detection means.
 7. The inventionaccording to claim 4 wherein said detection means comprises aphotographic plate.
 8. The invention according to claim 4 wherein saiddetection means comprises an array of X-ray detectors.
 9. A method ofobtaining X-ray interference patterns, comprising the steps of: a.directing a coherent monochromatic beam of X-rays from a point sourceonto a highly perfect laminar crystal not exceeding a prespecifiedthickness and having a plurality of parallel scattering planes therein;b. scattering said X-rays in all directions by the atoms within saidscattering planes; and c. positioning a detector parallel to saidscattering planes of said crystal so as to receive the scatteredradiation therefrom and whereon nonlocalized conical interferencefringes are detected by virtue of the path differences of the scatteredradiation between the detector and each of said scattering planes. 10.The invention according to claim 9 wherein said prespecified thicknessis defined by one-half of the square root of the product of thedetector-to-crystal distance and the scatter plane separation.